Initial boundary value problem of pseudo-parabolic Kirchhoff equations
with logarithmic nonlinearity
Abstract
In this paper, we consider the initial boundary value problem for a
pseudo-parabolic Kirchhoff equation with logarithmic nonlinearity. Using
the potential well method, we obtain a threshold result of global
existence and finite-time blow-up for the weak solutions with initial
energy J ( u 0 ) ≤ d . When the initial energy J ( u 0 ) >
d , we find another criterion for the vanishing solution and blow-up
solution. We also establish the decay rate of the global solution and
estimate the life span of the blow-up solution. Meanwhile, we study the
existence of the ground state solution to the corresponding stationary
problem.